.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/formulations/plot_sobieski_idf_example.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_formulations_plot_sobieski_idf_example.py: IDF-based MDO on the Sobieski SSBJ test case ============================================ .. GENERATED FROM PYTHON SOURCE LINES 24-35 .. code-block:: Python from __future__ import annotations from gemseo import configure_logger from gemseo import create_discipline from gemseo import create_scenario from gemseo import generate_n2_plot from gemseo.problems.sobieski.core.design_space import SobieskiDesignSpace configure_logger() .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 36-43 Instantiate the disciplines ---------------------------- First, we instantiate the four disciplines of the use case: :class:`.SobieskiPropulsion`, :class:`.SobieskiAerodynamics`, :class:`.SobieskiMission` and :class:`.SobieskiStructure`. .. GENERATED FROM PYTHON SOURCE LINES 43-50 .. code-block:: Python disciplines = create_discipline([ "SobieskiPropulsion", "SobieskiAerodynamics", "SobieskiMission", "SobieskiStructure", ]) .. GENERATED FROM PYTHON SOURCE LINES 51-54 We can quickly access the most relevant information of any discipline (name, inputs, and outputs) with Python's ``print()`` function. Moreover, we can get the default input values of a discipline with the attribute :attr:`.MDODiscipline.default_inputs` .. GENERATED FROM PYTHON SOURCE LINES 54-58 .. code-block:: Python for discipline in disciplines: print(discipline) print(f"Default inputs: {discipline.default_inputs}") .. rst-class:: sphx-glr-script-out .. code-block:: none SobieskiPropulsion Default inputs: {'c_3': array([4360.]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'x_3': array([0.5]), 'y_23': array([12562.01206488])} SobieskiAerodynamics Default inputs: {'c_4': array([0.01375]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'y_32': array([0.50279625]), 'y_12': array([5.06069742e+04, 9.50000000e-01]), 'x_2': array([1.])} SobieskiMission Default inputs: {'y_24': array([4.15006276]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'y_34': array([1.10754577]), 'y_14': array([50606.9741711 , 7306.20262124])} SobieskiStructure Default inputs: {'y_21': array([50606.9741711]), 'x_shared': array([5.0e-02, 4.5e+04, 1.6e+00, 5.5e+00, 5.5e+01, 1.0e+03]), 'y_31': array([6354.32430691]), 'c_2': array([6.]), 'x_1': array([0.25, 1. ]), 'c_0': array([2000.]), 'c_1': array([25000.])} .. GENERATED FROM PYTHON SOURCE LINES 59-63 You may also be interested in plotting the couplings of your disciplines. A quick way of getting this information is the API function :func:`.generate_n2_plot`. A much more detailed explanation of coupling visualization is available :ref:`here `. .. GENERATED FROM PYTHON SOURCE LINES 63-65 .. code-block:: Python generate_n2_plot(disciplines, save=False, show=True) .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_001.png :alt: plot sobieski idf example :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 66-75 Build, execute and post-process the scenario -------------------------------------------- Then, we build the scenario which links the disciplines with the formulation and the optimization algorithm. Here, we use the :class:`.IDF` formulation. We tell the scenario to minimize -y_4 instead of minimizing y_4 (range), which is the default option. Instantiate the scenario ^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 75-78 .. code-block:: Python design_space = SobieskiDesignSpace() design_space .. raw:: html
Sobieski design space:
Name Lower bound Value Upper bound Type
x_shared[0] 0.01 0.05 0.09 float
x_shared[1] 30000 45000 60000 float
x_shared[2] 1.4 1.6 1.8 float
x_shared[3] 2.5 5.5 8.5 float
x_shared[4] 40 55 70 float
x_shared[5] 500 1000 1500 float
x_1[0] 0.1 0.25 0.4 float
x_1[1] 0.75 1 1.25 float
x_2 0.75 1 1.25 float
x_3 0.1 0.5 1 float
y_14[0] 24850 50606.9741711 77100 float
y_14[1] -7700 7306.20262124 45000 float
y_32 0.235 0.5027962499999999 0.795 float
y_31 2960 6354.32430691 10185 float
y_24 0.44 4.15006276 11.13 float
y_34 0.44 1.10754577 1.98 float
y_23 3365 12194.2671934 26400 float
y_21 24850 50606.9741711 77250 float
y_12[0] 24850 50606.9742 77250 float
y_12[1] 0.45 0.95 1.5 float


.. GENERATED FROM PYTHON SOURCE LINES 79-87 .. code-block:: Python scenario = create_scenario( disciplines, "IDF", objective_name="y_4", design_space=design_space, maximize_objective=True, ) .. GENERATED FROM PYTHON SOURCE LINES 88-90 Set the design constraints ^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 90-93 .. code-block:: Python for c_name in ["g_1", "g_2", "g_3"]: scenario.add_constraint(c_name, "ineq") .. GENERATED FROM PYTHON SOURCE LINES 94-101 Visualize the XDSM ^^^^^^^^^^^^^^^^^^ Generate the XDSM file on the fly: - ``log_workflow_status=True`` will log the status of the workflow in the console, - ``save_html`` (default ``True``) will generate a self-contained HTML file, that can be automatically opened using ``show_html=True``. .. GENERATED FROM PYTHON SOURCE LINES 101-103 .. code-block:: Python scenario.xdsmize(save_html=False) .. raw:: html


.. GENERATED FROM PYTHON SOURCE LINES 104-108 Define the algorithm inputs ^^^^^^^^^^^^^^^^^^^^^^^^^^^ We set the maximum number of iterations, the optimizer and the optimizer options .. GENERATED FROM PYTHON SOURCE LINES 108-116 .. code-block:: Python algo_options = { "ftol_rel": 1e-10, "ineq_tolerance": 1e-3, "eq_tolerance": 1e-3, "normalize_design_space": True, } scn_inputs = {"max_iter": 20, "algo": "SLSQP", "algo_options": algo_options} .. GENERATED FROM PYTHON SOURCE LINES 117-119 Execute the scenario ^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 119-121 .. code-block:: Python scenario.execute(scn_inputs) .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 10:52:28: INFO - 10:52:28: *** Start MDOScenario execution *** INFO - 10:52:28: MDOScenario INFO - 10:52:28: Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure INFO - 10:52:28: MDO formulation: IDF INFO - 10:52:28: Optimization problem: INFO - 10:52:28: minimize -y_4(x_shared, y_14, y_24, y_34) INFO - 10:52:28: with respect to x_1, x_2, x_3, x_shared, y_12, y_14, y_21, y_23, y_24, y_31, y_32, y_34 INFO - 10:52:28: subject to constraints: INFO - 10:52:28: g_1(x_shared, x_1, y_31, y_21) <= 0.0 INFO - 10:52:28: g_2(x_shared, x_2, y_32, y_12) <= 0.0 INFO - 10:52:28: g_3(x_shared, x_3, y_23) <= 0.0 INFO - 10:52:28: y_31_y_32_y_34(x_shared, x_3, y_23): y_31(x_shared, x_3, y_23) - y_31 == 0.0 INFO - 10:52:28: y_32(x_shared, x_3, y_23) - y_32 == 0.0 INFO - 10:52:28: y_34(x_shared, x_3, y_23) - y_34 == 0.0 INFO - 10:52:28: y_21_y_23_y_24(x_shared, x_2, y_32, y_12): y_21(x_shared, x_2, y_32, y_12) - y_21 == 0.0 INFO - 10:52:28: y_23(x_shared, x_2, y_32, y_12) - y_23 == 0.0 INFO - 10:52:28: y_24(x_shared, x_2, y_32, y_12) - y_24 == 0.0 INFO - 10:52:28: y_12_y_14(x_shared, x_1, y_31, y_21): y_12(x_shared, x_1, y_31, y_21) - y_12 == 0.0 INFO - 10:52:28: y_14(x_shared, x_1, y_31, y_21) - y_14 == 0.0 INFO - 10:52:28: over the design space: INFO - 10:52:28: +-------------+-------------+--------------------+-------------+-------+ INFO - 10:52:28: | Name | Lower bound | Value | Upper bound | Type | INFO - 10:52:28: +-------------+-------------+--------------------+-------------+-------+ INFO - 10:52:28: | x_shared[0] | 0.01 | 0.05 | 0.09 | float | INFO - 10:52:28: | x_shared[1] | 30000 | 45000 | 60000 | float | INFO - 10:52:28: | x_shared[2] | 1.4 | 1.6 | 1.8 | float | INFO - 10:52:28: | x_shared[3] | 2.5 | 5.5 | 8.5 | float | INFO - 10:52:28: | x_shared[4] | 40 | 55 | 70 | float | INFO - 10:52:28: | x_shared[5] | 500 | 1000 | 1500 | float | INFO - 10:52:28: | x_1[0] | 0.1 | 0.25 | 0.4 | float | INFO - 10:52:28: | x_1[1] | 0.75 | 1 | 1.25 | float | INFO - 10:52:28: | x_2 | 0.75 | 1 | 1.25 | float | INFO - 10:52:28: | x_3 | 0.1 | 0.5 | 1 | float | INFO - 10:52:28: | y_14[0] | 24850 | 50606.9741711 | 77100 | float | INFO - 10:52:28: | y_14[1] | -7700 | 7306.20262124 | 45000 | float | INFO - 10:52:28: | y_32 | 0.235 | 0.5027962499999999 | 0.795 | float | INFO - 10:52:28: | y_31 | 2960 | 6354.32430691 | 10185 | float | INFO - 10:52:28: | y_24 | 0.44 | 4.15006276 | 11.13 | float | INFO - 10:52:28: | y_34 | 0.44 | 1.10754577 | 1.98 | float | INFO - 10:52:28: | y_23 | 3365 | 12194.2671934 | 26400 | float | INFO - 10:52:28: | y_21 | 24850 | 50606.9741711 | 77250 | float | INFO - 10:52:28: | y_12[0] | 24850 | 50606.9742 | 77250 | float | INFO - 10:52:28: | y_12[1] | 0.45 | 0.95 | 1.5 | float | INFO - 10:52:28: +-------------+-------------+--------------------+-------------+-------+ INFO - 10:52:28: Solving optimization problem with algorithm SLSQP: INFO - 10:52:28: 5%|▌ | 1/20 [00:00<00:00, 220.68 it/sec, obj=-536] INFO - 10:52:28: 10%|█ | 2/20 [00:00<00:00, 54.05 it/sec, obj=-1.49e+3] INFO - 10:52:28: 15%|█▌ | 3/20 [00:00<00:00, 57.85 it/sec, obj=-3.83e+3] INFO - 10:52:28: 20%|██ | 4/20 [00:00<00:00, 59.86 it/sec, obj=-3.96e+3] INFO - 10:52:28: 25%|██▌ | 5/20 [00:00<00:00, 61.27 it/sec, obj=-3.96e+3] INFO - 10:52:28: 30%|███ | 6/20 [00:00<00:00, 62.09 it/sec, obj=-3.96e+3] INFO - 10:52:28: 35%|███▌ | 7/20 [00:00<00:00, 62.61 it/sec, obj=-3.96e+3] INFO - 10:52:28: 40%|████ | 8/20 [00:00<00:00, 63.04 it/sec, obj=-3.96e+3] INFO - 10:52:28: 45%|████▌ | 9/20 [00:00<00:00, 67.25 it/sec, obj=-3.96e+3] INFO - 10:52:28: 50%|█████ | 10/20 [00:00<00:00, 66.92 it/sec, obj=-3.96e+3] INFO - 10:52:28: 55%|█████▌ | 11/20 [00:00<00:00, 70.35 it/sec, obj=-3.96e+3] INFO - 10:52:28: 60%|██████ | 12/20 [00:00<00:00, 73.29 it/sec, obj=-3.96e+3] INFO - 10:52:28: 65%|██████▌ | 13/20 [00:00<00:00, 76.13 it/sec, obj=-3.96e+3] INFO - 10:52:28: 70%|███████ | 14/20 [00:00<00:00, 78.80 it/sec, obj=-3.96e+3] INFO - 10:52:28: 75%|███████▌ | 15/20 [00:00<00:00, 81.27 it/sec, obj=-3.96e+3] INFO - 10:52:28: 80%|████████ | 16/20 [00:00<00:00, 83.57 it/sec, obj=-3.96e+3] INFO - 10:52:28: 85%|████████▌ | 17/20 [00:00<00:00, 85.72 it/sec, obj=-3.96e+3] INFO - 10:52:28: 90%|█████████ | 18/20 [00:00<00:00, 87.72 it/sec, obj=-3.96e+3] INFO - 10:52:28: 95%|█████████▌| 19/20 [00:00<00:00, 89.55 it/sec, obj=-3.96e+3] INFO - 10:52:28: 100%|██████████| 20/20 [00:00<00:00, 91.29 it/sec, obj=-3.96e+3] INFO - 10:52:28: Optimization result: INFO - 10:52:28: Optimizer info: INFO - 10:52:28: Status: 8 INFO - 10:52:28: Message: Positive directional derivative for linesearch INFO - 10:52:28: Number of calls to the objective function by the optimizer: 21 INFO - 10:52:28: Solution: INFO - 10:52:28: The solution is feasible. INFO - 10:52:28: Objective: -3963.909125280606 INFO - 10:52:28: Standardized constraints: INFO - 10:52:28: g_1 = [-0.01807265 -0.03335477 -0.04425595 -0.0518399 -0.05733055 -0.13720865 INFO - 10:52:28: -0.10279135] INFO - 10:52:28: g_2 = 7.162693463458325e-06 INFO - 10:52:28: g_3 = [-7.67188159e-01 -2.32811841e-01 -3.73860557e-05 -1.83255000e-01] INFO - 10:52:28: y_12_y_14 = [ 1.12943503e-05 4.28787041e-07 1.13267743e-05 -1.50426345e-05] INFO - 10:52:28: y_21_y_23_y_24 = [-2.77708306e-16 1.33085464e-05 -2.62473913e-05] INFO - 10:52:28: y_31_y_32_y_34 = [-2.35661889e-06 -2.32437808e-06 1.57269783e-05] INFO - 10:52:28: Design space: INFO - 10:52:28: +-------------+-------------+---------------------+-------------+-------+ INFO - 10:52:28: | Name | Lower bound | Value | Upper bound | Type | INFO - 10:52:28: +-------------+-------------+---------------------+-------------+-------+ INFO - 10:52:28: | x_shared[0] | 0.01 | 0.06000179067336589 | 0.09 | float | INFO - 10:52:28: | x_shared[1] | 30000 | 60000 | 60000 | float | INFO - 10:52:28: | x_shared[2] | 1.4 | 1.4 | 1.8 | float | INFO - 10:52:28: | x_shared[3] | 2.5 | 2.5 | 8.5 | float | INFO - 10:52:28: | x_shared[4] | 40 | 70 | 70 | float | INFO - 10:52:28: | x_shared[5] | 500 | 1500 | 1500 | float | INFO - 10:52:28: | x_1[0] | 0.1 | 0.4 | 0.4 | float | INFO - 10:52:28: | x_1[1] | 0.75 | 0.75 | 1.25 | float | INFO - 10:52:28: | x_2 | 0.75 | 0.75 | 1.25 | float | INFO - 10:52:28: | x_3 | 0.1 | 0.156238904271528 | 1 | float | INFO - 10:52:28: | y_14[0] | 24850 | 44749.85202975167 | 77100 | float | INFO - 10:52:28: | y_14[1] | -7700 | 19351.86291108692 | 45000 | float | INFO - 10:52:28: | y_32 | 0.235 | 0.7328131425977524 | 0.795 | float | INFO - 10:52:28: | y_31 | 2960 | 9437.362336215188 | 10185 | float | INFO - 10:52:28: | y_24 | 0.44 | 8.05763183450019 | 11.13 | float | INFO - 10:52:28: | y_34 | 0.44 | 0.9239115967364436 | 1.98 | float | INFO - 10:52:28: | y_23 | 3365 | 5553.60943830111 | 26400 | float | INFO - 10:52:28: | y_21 | 24850 | 44749.85202975168 | 77250 | float | INFO - 10:52:28: | y_12[0] | 24850 | 44749.85202975167 | 77250 | float | INFO - 10:52:28: | y_12[1] | 0.45 | 0.9027908995968825 | 1.5 | float | INFO - 10:52:28: +-------------+-------------+---------------------+-------------+-------+ INFO - 10:52:28: *** End MDOScenario execution (time: 0:00:00.262063) *** {'max_iter': 20, 'algo_options': {'ftol_rel': 1e-10, 'ineq_tolerance': 0.001, 'eq_tolerance': 0.001, 'normalize_design_space': True}, 'algo': 'SLSQP'} .. GENERATED FROM PYTHON SOURCE LINES 122-126 Save the optimization history ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ We can save the whole optimization problem and its history for further post processing: .. GENERATED FROM PYTHON SOURCE LINES 126-128 .. code-block:: Python scenario.save_optimization_history("idf_history.h5", file_format="hdf5") .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 10:52:28: Export optimization problem to file: idf_history.h5 .. GENERATED FROM PYTHON SOURCE LINES 129-130 We can also save only calls to functions and design variables history: .. GENERATED FROM PYTHON SOURCE LINES 130-132 .. code-block:: Python scenario.save_optimization_history("idf_history.xml", file_format="ggobi") .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 10:52:28: Export to ggobi for functions: ['-y_4', 'g_1', 'g_2', 'g_3', 'y_12_y_14', 'y_21_y_23_y_24', 'y_31_y_32_y_34'] INFO - 10:52:28: Export to ggobi file: idf_history.xml .. GENERATED FROM PYTHON SOURCE LINES 133-135 Print optimization metrics ^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 135-137 .. code-block:: Python scenario.print_execution_metrics() .. rst-class:: sphx-glr-script-out .. code-block:: none INFO - 10:52:28: Scenario Execution Statistics INFO - 10:52:28: Discipline: SobieskiPropulsion INFO - 10:52:28: Executions number: 20 INFO - 10:52:28: Execution time: 0.010683990007237298 s INFO - 10:52:28: Linearizations number: 9 INFO - 10:52:28: Discipline: SobieskiAerodynamics INFO - 10:52:28: Executions number: 20 INFO - 10:52:28: Execution time: 0.014151883005979471 s INFO - 10:52:28: Linearizations number: 9 INFO - 10:52:28: Discipline: SobieskiMission INFO - 10:52:28: Executions number: 20 INFO - 10:52:28: Execution time: 0.001008952000120189 s INFO - 10:52:28: Linearizations number: 9 INFO - 10:52:28: Discipline: SobieskiStructure INFO - 10:52:28: Executions number: 20 INFO - 10:52:28: Execution time: 0.08012645499911741 s INFO - 10:52:28: Linearizations number: 9 INFO - 10:52:28: Total number of executions calls: 80 INFO - 10:52:28: Total number of linearizations: 36 .. GENERATED FROM PYTHON SOURCE LINES 138-140 Plot the optimization history view ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 140-142 .. code-block:: Python scenario.post_process("OptHistoryView", save=True, show=True) .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 143-145 Plot the quadratic approximation of the objective ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 145-146 .. code-block:: Python scenario.post_process("QuadApprox", function="-y_4", save=False, show=True) .. rst-class:: sphx-glr-horizontal * .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_002.png :alt: Hessian matrix SR1 approximation of -y_4 :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_002.png :class: sphx-glr-multi-img * .. image-sg:: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_003.png :alt: plot sobieski idf example :srcset: /examples/formulations/images/sphx_glr_plot_sobieski_idf_example_003.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 4.846 seconds) .. _sphx_glr_download_examples_formulations_plot_sobieski_idf_example.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_sobieski_idf_example.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_sobieski_idf_example.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_